Einstein’s mistakes

In addition to his well-accepted results, some of Einstein’s papers contain mistakes:

• 1905: In the original German version of the special relativity paper, and in some English translations, Einstein gives a wrong expression for the transverse mass of a fast moving particle. The transverse mass is the antiquated name for the ratio of the 3-force to the 3-acceleration when the force is perpendicular to the velocity. Einstein gives this ratio as , while the actual value is (corrected by Max Planck).
• 1905: In his PhD dissertation, the friction in dilute solutions has a miscalculated numerical prefactor, which makes the estimate of Avogadro’s number off by a factor of 3. The mistake is corrected by Einstein in a later publication.
• 1905: An expository paper explaining how airplanes fly includes an example which is incorrect. There is a wing which he claims will generate lift. This wing is flat on the bottom, and flat on the top, with a small bump at the center. It is designed to generate lift by Bernoulli’s principle, and Einstein claims that it will. Simple action reaction considerations, though, show that the wing will not generate lift, at least if it is long enough.
• 1911: Einstein predicted how much the sun’s gravity would deflect nearby starlight, but used an approximation which gives an answer which is half as big as the correct one.^[74]
• 1913: Einstein started writing papers based on his belief that the hole argument made general covariance impossible in a theory of gravity.
• 1922: Einstein published a qualitative theory of superconductivity based on the vague idea of electrons shared in orbits. This paper predated modern quantum mechanics, and is well understood to be completely wrong. The correct BCS theory of low temperature superconductivity was only worked out in 1957, thirty years after the establishing of modern quantum mechanics.
• 1937: Einstein believed that the focusing properties of geodesics in general relativity would lead to an instability which causes plane gravitational waves to collapse in on themselves. While this is true to a certain extent in some limits, because gravitational instabilities can lead to a concentration of energy density into black holes, for plane waves of the type Einstein and Rosen considered in their paper, the instabilities are under control. Einstein retracted this position a short time later, but until his death his collaborator Nathan Rosen maintained that gravitational waves are unstable.
• 1939: Einstein denied several times that black holes could form, the last time in print. He published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein’s argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse. But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined.

In addition to these well-established mistakes, there are other arguments whose deduction is considered correct, but whose interpretation or philosophical conclusion is considered to have been incorrect:

• In the Bohr–Einstein debates and the papers following this, Einstein tries to poke holes in the uncertainty principle, ingeniously, but unsuccessfully.
• In the EPR paper, Einstein concludes that quantum mechanics must be replaced by local hidden variables. The measured violations of Bell’s inequality show that hidden variables, if they exist, must be nonlocal.

Einstein himself considered the use of the "fudge factor" lambda in his 1917 paper founding cosmology as a "blunder".^[74] The theory of general relativity predicted an expanding or contracting universe, but Einstein wanted a universe which is an unchanging three dimensional sphere, like the surface of a three dimensional ball in four dimensions. He wanted this for philosophical reasons, so as to incorporate Mach’s principle in a reasonable way. He stabilized his solution by introducing a cosmological constant, and when the universe was shown to be expanding, he retracted the constant as a blunder. This is not really much of a blunder – the cosmological constant is necessary within general relativity as it is currently understood, and it is widely believed to have a nonzero value today. Einstein took the wrong side in a few scientific debates.

• He briefly flirted with transverse and longitudinal mass concepts, before rejecting them.
• Einstein initially opposed Minkowski’s geometrical formulation of special relativity, changing his mind completely a few years later.
• Based on his cosmological model, Einstein rejected expanding universe solutions by Friedman and Lemaitre as unphysical, changing his mind when the universe was shown to be expanding a few years later.
• Finding it too formal, Einstein believed that Heisenberg’s matrix mechanics was incorrect. He changed his mind when Schrödinger and others demonstrated that the formulation in terms of the Schrödinger equation, based on Einstein’s wave-particle duality was equivalent to Heisenberg’s matrices.
• Einstein rejected work on black holes^[75] by Chandrasekhar, Oppenheimer, and others, believing, along with Eddington, that collapse past the horizon (then called the ’Schwarzschild singularity’) would never happen. So big was his influence, that this opinion was not rejected until the early 1960s, almost a decade after his death.
• Einstein believed that some sort of nonlinear instability could lead to a field theory whose solutions would collapse into pointlike objects which would behave like quantum particles. While there are many field theories with point-like particle solutions, none of them behave like quantum particles. It is widely believed that quantum mechanics would be impossible to reproduce from a local field theory of the type Einstein considered, because of Bell’s inequality.

In addition to these well known mistakes, it is sometimes claimed that the general line of Einstein’s reasoning in the 1905 relativity paper is flawed, or the photon paper, or one or another of the most famous papers. None of these claims are widely accepted